In the following equation, x, t and F represent respectively, displacement, time and force:
`F = a + bt + (1)/(c+d. x)+ Asin(omegat+phi)`
The dimensional formula for A. d is

Options

A. `[T^(-1)]`
B. `[L^(-1)]`
C. `[M^(-1)]`
D. `[TL^(-1)]`

Answer

B

Explanation

`F= a+ bt+ (1)/(c+d.x)+ Asin(omegat+phi)`
As `sin(omegat+phi)` is dimensionless, therefore A has dimensions of force.
`:. [A]= [F]= [MLT^(-2)]`
As each term on RHS represents force
`:. (1)/(c+d. x)= F` or `(1)/(c)= F`
`:. [c]= (1)/([F])= (1)/([MLT^(-2)]= [M^(-1)L^(-1)T^(2)]`
As c is added to d.x therefore dimension of c are same that of d.x
`:. [d.x]= [c]` or `[d]= ([c])/([x])= ([M^(-1)L^(-1)T^(2)])/([L])= [M^(-1)L^(-2)T^(2)]`
The dimensional formula for `A.d = [MLT^(-2)][M^(-1)L^(-2)T^(2)]= [L^(-1)]`